Inventiones mathematicae

, Volume 151, Issue 3, pp 611–664

Homotopy equivalences of p-completed classifying spaces of finite groups


  • Carles Broto
    • Departament de Matemàtiques, Universitat Autònoma de Barcelona, E–08193 Bellaterra, Spain (e-mail:
  • Ran Levi
    • Department of Mathematical Sciences, University of Aberdeen, Meston Building 339, Aberdeen AB24 3UE, UK (e-mail:
  • Bob Oliver
    • LAGA, Institut Galilée, Av. J-B Clément, 93430 Villetaneuse, France (e-mail:

DOI: 10.1007/s00222-002-0264-5

Cite this article as:
Broto, C., Levi, R. & Oliver, B. Invent. math. (2003) 151: 611. doi:10.1007/s00222-002-0264-5


We study homotopy equivalences of p-completions of classifying spaces of finite groups. To each finite group G and each prime p, we associate a finite category ℒpc(G) with the following properties. Two p-completed classifying spaces BGp and BGp have the same homotopy type if and only if the associated categories ℒpc(G) and ℒpc(G’) are equivalent. Furthermore, the topological monoid Aut(BGp) of self equivalences is determined by the self equivalences of the associated category ℒpc(G).

Mathematical Subject Classification (1991): 55R35, 55R40, 55Q52

Copyright information

© Springer-Verlag Berlin Heidelberg 2002